what is m^3-3m^2=5m-15 factored?

Question

 i cant seem to figure this out

Answer 1

What is m^3 – 3m^2 = 5m – 15 factored?

 

It's interesting that the problem was posed this way because you might notice that you can use the Distributive Property on both sides:

 

m^2(m – 3) = 5(m – 3)

 

At this point you might decide to say "If m ≠ 3 then I can divide both sides by (m–3) to get m^2 = 5, where m = ±√(5) are the only two answers."

 

However, if instead you subtracted 5(m – 3) from both sides:

 

m^2(m – 3) – 5(m – 3) = 0

 

and used the Distributive Property:

 

(m – 3)(m^2 – 5) = 0

 

Substitute (√(5))^2 for 5:

 

(m – 3)(m^2 – (√(5))^2) = 0

 

Use Difference of Squares:

 

(m – 3)(m + √(5))(m – √(5)) = 0

 

That's the answer to, "What is m^3 – 3m^2 = 5m – 15 factored?"

 

But now, using the Zero Product Property, you can find the values of m that make it true:

 

(m – 3) = 0 ==> m = 3

(m – √(5)) = 0 ==> m = + √(5)

(m + √(5)) = 0 ==> m = – √(5)

Answer 2

Hi Tabalina;

m^3-3m^2=5m-15

Let's bring everything to one side...

m³-3m²-5m+15=0

For the FOIL...

FIRST must be (m²)(m)=m³

(m²...)(m...)

OUTER must be (-3)(m²)=-3m²

(m²...)(m-3)

INNER must be (-5)(m)=-5m

(m²-5)(m-3)

LAST must be (-5)(-3)=15

0=(m²-5)(m-3)

Either or both parenthetical equation(s) must equal zero...

0=m²-5.........0=m-3

5=m²............3=m

+/- √5=m

Please remember that - √5, when squared, produces the same result as +√5, when squared.

There are three answers...

m=-√5, +√5 and 3

 

 

Answer 3

The first step is to reorganize the equation to get a zero on the right hand side

 

m³ - 3m² - 5 m + 15  = 0

 

The cubic expression on the left hand side can be factored by a method called factoring by grouping.

This method does not always work, but is very good when it does.

 

Step 1:   pull a factor of m² out of the first two terms   m² (m -3)

Step 2:   pull a factor of -5 out of the last two terms     -5(m-3)

Step 3:   {this is the good part}  notice that in both  steps 1 and 2 we got a factor of (m-3)

Step 4:  take advantage of this good fortune to write the whole expression as (m-3) ( m² -5)

           This ends the factor by grouping part

Step 5:   m² -5   factors as  (m- sqrt(5) ) (m + sqrt(5))

 

Final answer (m-3) (m - sqrt(5)) ( m+ sqrt(5))  = 0

 

  So the solutions to the problem are

       m = 3

      m = - sqrt(5)

      m = + sqrt(5)